WASHINGTON (AP) — Sen. Marco Rubio, R-Fla., sought support from House conservatives Wednesday for far-reaching immigration legislation, but many lawmakers emerged from their meeting deeply skeptical of any comprehensive bill with a pathway to citizenship for immigrants here illegally.

It underscored the challenges ahead for the immigration bill and for Rubio himself as he ramps up his sales job to conservatives ahead of Senate floor debate on the legislation beginning next week.

“I cannot vote for a bill that gives amnesty to illegal aliens here in this country. Will not. I think there are a lot of conservatives that are in that position,” said Rep. Paul Broun, R-Ga., after hearing from Rubio and other senators at a meeting in the basement of the Capitol organized by the Republican Study Committee, a group of House conservatives.

And House Judiciary Committee Chairman Bob Goodlatte, R-Va., said that the Senate bill written by Rubio and seven other senators in a bipartisan group “has a long way to go from the House perspective.”

Rubio, a tea party favorite and potential presidential candidate who’s acted as the bill’s emissary to the conservative community, has been saying for weeks that the bill needs stronger border security provisions in order to pass the House. Recently he’s said that it lacks the 60 votes needed to pass the Senate without improvements and that he himself wouldn’t be able to support it in its current form, even though he helped write it.

His comments have jarred immigration advocates, who’ve questioned his commitment to the legislation and voiced concerns that increased emphasis on border security could make the path to citizenship for some 11 million immigrants here illegally unachievable. The bill, supported by President Barack Obama, also seeks to overhaul legal immigration and visa programs and require all employers to check workers’ legal status.

Rubio objected Wednesday to the suggestion his comments could be complicating efforts on the bill.

“What’s stymying efforts in the Senate is not my comments. What’s stymying efforts in the Senate is we don’t have the votes to pass it because too many members on both sides of the aisle do not believe it goes far enough on border security,” Rubio told reporters after his meeting with House Republicans.

“So it’s very simple,” Rubio said. “If people want immigration reform, we’re going to have to improve the border security elements of the bill and we’re going to have to make people confident that what we’re doing is enough. And that’s what I’m going to focus on.”

Aware of the difficulty of winning over conservatives in the Republican-led House, Rubio and other supporters of the immigration bill are working to get a resounding vote of support in the Democratic-led Senate, including from many Republicans. The hope is that if the bill passes with some 70 lawmakers in favor, the House would be pressured to act.

For Rubio, helping secure those Senate votes is emerging as a test of his influence over fellow Republicans that may also help determine the fate of his presidential ambitions.

He has spent recent weeks meeting individually with Republican senators to discuss strengthening the legislation in ways that could get them on board, working with a list of 15 to 20 Republican senators who potentially could be persuaded to vote for the bill. He’s also promoted the legislation with numerous TV and radio appearances.

Rubio’s challenge is to maintain the support of the tea party backers who lend him credibility and leverage in the immigration debate, while also getting credit for pushing a landmark piece of legislation that’s opposed by many in the tea party but is a priority to the Latino voters who increasingly help determine the outcome of presidential elections.

Rubio supported efforts by Sen. John Cornyn, R-Texas, on an amendment Cornyn unveiled Wednesday to enact tough new border requirements, including a biometric exit system at all airports and seaports, before any immigrant here illegally could achieve permanent legal residence. Sens. Tom Coburn, R-Okla., and Rob Portman, R-Ohio, also said they’d met with Rubio to discuss their concerns over border security and enforcement, and Portman said he was weighing amendments to address them.

One change Rubio has focused on would give Congress, instead of the Homeland Security Department, a bigger role in creating a border security plan since many Republicans are skeptical of the Obama administration’s commitment to enforcing border security. As he described it on talk radio’s “Hugh Hewitt Show” on Tuesday, the plan would be legislated as part of the immigration bill, although other Republicans, including Sen. Rand Paul, R-Ky., have discussed having Congress vote on whether the border has been secured.